Large symmetry groups in quantum many-body systems could strongly enhance quantum fluctuations and provide a novel direction to stabilize exotic quantum phases beyond the conventional magnetic frustration. Motivated by recent progress in ultracold-atom systems and solid-state materials, we intertwine the SU(N) symmetry and frustration on both honeycomb and triangular antiferromagnets and integrate them through tuning the J1-J2 Heisenberg interactions. With the large-N analysis and self-consistent calculations, we obtain a rich phase diagram strictly satisfying the local constraints. It is shown that the system always favors topological chiral spin liquids for large enough N regardless of the lattice type. For small flavor numbers, the competition with the frustration induces a plethora of intermediate states even in the triangular limit, including Dirac spin liquid, valence cluster solids, flux ordered state and stripe states. The physical properties of each phase are discussed. We also explore the experimental realization and detection on relevant platforms.
[1] X.-P. Yao, R.-R. Luo, and G. Chen, Phys. Rev. B 105, 024401 (2022)
[2] X.-P. Yao, Y. Gao, and G. Chen, Phys. Rev. Research 3, 023138 (2021)